(a) Field of the Invention
This invention pertains generally to encoding of binary signals, and in particular, to a technique of encoding a sequence of bits for transmission on a quadrature amplitude modulated (QAM) carrier signal, in which nonlinear convolutional encoding and mapping of the encoder output to an expanded set of signalling alphabets are used to reduce the effect of channel impairments without sacrificing data rate or requiring more bandwidth, and in which differential encoding is used to remove the effect of the phase ambiguities of the expanded set of signalling alphabets.
(b) Description of the Prior Art
U.S. Pat. No. 4,077,021 issued to I. P. Csajka and G. Ungerboeck on Feb. 18, 1978, which is incorporated herein by reference, describes a technique for converting a sequence of binary digits into a sequence of signalling alphabets of a modulated carried signal for data transmission. The invention is intended to allow recovery of the original data even in situations where the transmission medium is severely impaired. Generally speaking, the Ungerboeck invention involves applying groups of r input bits to a finite state machine which is arranged to expand each input group into an r+1 bit group in accordance with predetermined linear logical combinations with certain bits in previous groups. The number P of bits stored in the encoder that are used to form the encoder output determine the number m(=2.sup.p) of states that the encoder may assume. Transitions from each encoder state to other states must follow prescribed rules. Accordingly, when the output of a convolutional encoder is subsequently used to modulate a carrier signal in accordance with in-phase and quadrature phase coordinates obtained by mapping the output of the convolutional encoder to an "expanded" set of 2.sup.r+1 signalling alphabets (sometimes referred to as an expanded signal constellation), the sequence of signalling alphabets must follow prescribed rules. The constellation is referred to as "expanded"because, conventionally, in order to transmit r bits in a signalling interval, a signal constellation of 2.sup.r signalling alphabets would suffice. At the receiver, the effect of impairments in the transmission medium which would otherwise impede data recovery are largely overcome by a maximum-likelihood decoding algorithm which determines the correct transmitted data using knowledge of the valid sequences of signalling alphabets. A discussion of one such decoding algorithm is contained in a paper by G. D. Forney Jr. entitled "The Viterbi Algorithm", Proc. of IEEE, Vol. 61, No. 3, March 1973, pp. 268-278.
Despite the advantages obtained by use of the encoding technique described by Csajka and Ungerboeck, phase hits or jumps occurring in the transmission medium may result, after recovery of equalization and carrier, in a rotation of the received signalling alphabets as compared to the initial determination of phase. This ambiguity in phase can cause errors in all subsequently received data and thereby seriously degrade the performance of the system. To avoid this problem, it would be desirable to apply a differential encoding technique to the original input data so that the received signalling alphabets, even after a rotation, can be used to recover the original data. One approach to differentially convolutional channel coding was developed by the present applicant and is described in a patent application Ser. No. 486,081, entitled "Differentially Convolutional Channel Coding with Expanded Set of Signalling Alphabets", filed on Apr. 18, 1983, now U.S. Pat. No. 4,483,012 which is incorporated herein by reference. In accordance with that invention, a binary signal, which may be initially scrambled in accordance with known techniques, is applied to a differential encoder which transforms each group of r input bits into an associated group of r differentially encoded bits, which is functionally related to the values of the current r input bits and some of the previous differentially encoded bits. The r bit output of the differential encoder is then applied to a convolutional encoder which expands each group into r+1 bits in accordance with predetermined logical combinations with certain bits in previous differential encoded groups; the output of the convolutional encoder permits only certain sequences of r+1 bit groups. The r+1 bit group is then used to determine coordinates u.sub.n and v.sub.n which respectively determine the amplitudes of the in-phase and quadrature phase carriers. Conceptually, these coordinates are determined by mapping each r+1 bit group output from the convolutional encoder to a signalling alphabet in an expanded signal constellation of 2.sup.r+1 signalling alphabets using a mapping strategy which insures that (1) the minimum distance between sequences of signalling alphabets corresponding to the sequences of r+1 bit outputs of the convolutional encoder is maximized and (2) if the sequence of signalling alphabets at the output of the mapping device is rotated by 180 degrees (or equivalently, the coordinates u.sub.n and v.sub.n of all the mapped signalling alphabets are inverted), the original input sequence of binary digits to the differential encoder can be recovered by applying the corresponding convolutional decoding and differential decoding operations to the sequence of received rotated signalling alphabets. Alternatively, the second principle recited above may be expressed as requiring that the effect of inversion of certain bits at the input to the convolutional encoder must be the same as a 180 degree rotation of the sequence of signalling alphabets at the output of the mapping device.
Applicant's previous invention was satisfactory when the signal constellations had only 180 degree phase ambiguity. However, the invention could not be practiced with constellations which have 90, 180 and 270 degree phase ambiguities, for example, the constellations shown in FIGS. 4 and 10-13. The latter kind of signal constellations can usually better deal with various channel impairments as compared to the former kind of constellations, given that the phase ambiguities of the signal constellations are not a problem.
In view of the foregoing, it is the broad object of the present invention to provide a technique and apparatus for converting a sequence of binary digits into a sequence of signalling alphabets of a modulated carrier for transmission on a medium subject to impairments such as phase hits and phase jumps, so that the original data can be accurately recovered. Specifically, it is desired to combine the advantages obtained by encoding as taught by Csajka and Ungerboeck with those associated with differential encoding in a system in which the expanded signal constellation can have 90, 180 and 270 degree phase ambiguities.